Number of Handshakes

What this combinatorics puzzle tests

This is an easy puzzle that appears frequently in quant and finance interviews as a warm-up or filter question. It tests whether you can quickly translate a real-world scenario into a counting problem and apply basic combinatorial reasoning without over-complicating it.

The key skill is recognizing that you're counting pairs of distinct objects from a fixed set, and avoiding the common trap of double-counting. Interviewers value clean, confident reasoning here—a clear explanation of why your formula works matters more than speed.

• Combinations and the binomial coefficient
• Symmetry and avoiding double-counting
• Translating word problems into mathematical notation